Finding paths and deleting edges in directed acyclic graphs
Information Processing Letters
Maintenance of transitive closures and transitive reductions of graphs
Proceedings of the International Workshop WG '87 on Graph-theoretic concepts in computer science
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STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
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SIAM Journal on Computing
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FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
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FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
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Journal of Experimental Algorithmics (JEA)
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SIAM Journal on Computing
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ESA'07 Proceedings of the 15th annual European conference on Algorithms
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
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CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
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This paper presents a new deterministic algorithm for decremental maintenance of the transitive closure in a directed graph. The algorithm processes any sequence of edge deletions in O(mn) time and answers queries in constant time. Until now such time bound has only been achieved by a randomized Las Vegas algorithm. In addition to that, a few decremental algorithms for maintaining strongly connected components are shown, whose time complexity is O(n1.5) for planar graphs, O(n log n) for graphs with bounded treewidth and O(mn) for general digraphs.